Impact of straight, unconnected, radially-oriented, and tapered mesopores on column efficiency: A theoretical investigation

- The impact of radially oriented mesopores (ROMs) on separation performance is studied.
- Both ends open ROMs cause an intra-particle diffusion hindrance factor of 23.
- One end close ROMs cause an intra-particle diffusion hindrance factor of 27.
- Particles with narrow ROMs are well suited for small molecules at optimum velocity.
- Particles with wide and tapered ROMs are ideal for large molecules at high velocities.

Superficially porous particles (SPPs) can be prepared from a pseudomorphic transformation (PMT) which produces straight, unconnected, and radially-oriented mesopores (ROMs). ROMs can be either both ends open in fully porous particles (FPPs) or one-end-closed in SPPs. The impact of ROMs on the longitudinal diffusion (B/u), solid-liquid mass transfer resistance (Csu), and on the eddy dispersion (A(u)) height equivalent to a theoretical plate (HETP) of 3D randomly packed columns was investigated based on theoretical viewpoints. Torquato's theory of effective diffusion in packed beds (B term), Giddings' coupling theory of eddy dispersion (A term), and Giddings' generalized nonequilibrium theory (Cs term) are applied to make predictions. First, it is found that the A term is nearly independent on the internal structure of the particle. Secondly, in the absence of flow, infinitely narrow and both ends open (no constriction effect) ROMs induce an internal hindrance factor of 23 regarding diffusion along the axial direction. Experimental data reveal that one-end-closed and 80 Å wide ROMs in SPPs lead to a measurable internal hindrance factor of 27 regarding diffusion in the porous shell. Thirdly, above the optimum speed, the Cs coefficient is dependent on the geometry (cylinders, cones, etc.) of the ROMs: when ROMs are conical in SPPs, Cs is expected to decrease by 80% with respect to cylindrical ROMs. From an application perspective, PMT-SPPs prepared with narrow ROMs are well suited for the analysis of small molecules at or below optimum speed (lowest B term) while PMT-SPPs made of wide and conical ROMs are ideal for the analysis of large molecules above optimum speed (smallest Cs term).